As Obama prepared to tour a missile battery that is part of Israel's Iron Dome defenses, an aide at the Tel Aviv airport directed him to follow the red line on the tarmac.
"Bibi's always talking to me about red lines," Obama quipped, referring to Netanyahu by his familiar name.
Netanyahu has set "red lines" on Iran's nuclear development capabilities. Israel repeatedly has threatened to take military action should Iran appear to be on the verge of developing a bomb. The U.S. has pushed for more time to allow diplomacy and economic penalties to run their course, though Obama insists military action is an option. The issue has become a point of tension between the two allies.
Obama himself has used the phrase to describe limits that could prompt action against the Syrian government. Any use of chemical weapons by Syria, Obama has said, would constitute a "red line" that if breached could prompt direct U.S. intervention. It's a threat that could be tested amid new accusations that the regime used chemicals in an attack in a village in the north of Syria.
Referring to the painted red lines at the airport, Obama joked that it was "a psychological ploy."
Netanyahu replied: "It was minutely planned."
His tone turned serious hours later, during a news conference with Obama, when he was asked about their banter about "red lines."
"We did have a joke about that but obviously this matter is no joke," Netanyahu said.
Obama found a lighthearted way to poke fun at his Israeli counterpart as he thanked Netanyahu, his wife and two sons for the welcome they gave him at the airport.
"I did inform the prime minister that they are very good-looking young men, who clearly got their looks from their mother," Obama said at the news conference, prompting laughter from the government officials and reporters in the room.
Before Obama could continue, Netanyahu shot back: "I could say the same thing of your daughters."
Never one to relinquish a chance to show common ground, Obama said he and the Israeli leader had a shared strategy when it comes to matrimony.
"Our goal is to improve our gene pool by marrying women who are better than we are," he said.
Obama received a rock star's welcome at Israel's international airport from Netanyahu, Israeli President Shimon Peres and other dignitaries.
Netanyahu's new Cabinet, seated just two days ago, lined up and excitedly shook hands with the president, who chatted with each one as he moved down the line.
There were no signs of the sometimes frostiness between Netanyahu and Obama. The two smiled, joked and warmly exchanged pleasantries throughout the day.
In his speech at the airport, Netanyahu kidded Obama about his desire to explore Israel incognito. Netanyahu said he could arrange a trip to the bars and cafes of Tel Aviv. "We even prepared a fake moustache for you," he said.
When Obama visits the West Bank on Thursday, the Palestinians will send a message of music and peace.
Dozens of Palestinians will perform the traditional Dabka dance for Obama at the Palestinian Youth Center El-Bireh. The dancers were busy practicing on Wednesday.
Obama is set to meet with 120 youths chosen from four centers across the West Bank that are funded by the State Department's development arm, the U.S. Agency for International Development. After that, he will meet with seven of them for half an hour.
Saja Abdelraheem, one of the lucky seven, said she'll tell Obama she "has a dream" of seeing the conflict with Israel end during his term.
"I will ask him what can he do to make our dream come true, living in an independent state, ending our daily suffering," the 23-year-old said.
Mohammed Nazal, 28, who also will meet Obama, said: "I'm going to tell him that we want to live in peace and dignity, to work, build, move freely and in peace."
Among the guests invited to dine Thursday with America's first black president is Israel's first black beauty queen.
Yityish "Titi" Aynaw, 21, who was named Miss Israel three weeks ago, is the first Ethiopian-born Israeli to wear the crown.
Israel began airlifting Ethiopian Jews the fabled descendants of the Israelite tribe of Dan three decades ago, but the community has complained of discrimination and has still struggled to integrate into Israeli society.
Aynaw hopes to be a role model to her immigrant community and says President Obama is her role model. In high school, she researched his biography and wrote a paper about his accomplishments.
President Shimon Peres has invited her to attend Thursday night's state dinner. She said if she gets a chance to speak to the U.S. leader, she'll thank him for inspiring her.
"He paved a road, for people who want to dream and go far," Aynaw told Israel's Channel 2 TV.
It's no secret that Obama is left handed. But, he confessed to Netanyahu, it wasn't always easy to be a southpaw.
As Obama signed a guest book at Netanyahu's residence, the Israeli prime minister took note of Obama's distinctive inverted writing style.
Obama said that in Indonesia, where he lived as a child, using your left hand was considered bad manners and that instructors tried to correct it.
He said he stuck with it "even though I would get hit with the rulers."
Israelis and others awaiting Obama's arrival at the airport were surprised to see his signature black limousine sitting on the back of a flatbed truck.
The U.S. Secret Service said the vehicle suffered mechanical problems before Obama arrived but the agency wouldn't say what happened. Mechanics were examining the vehicle.
The disabled limo was swapped out for a backup, and Obama went ahead with a busy day in Tel Aviv and Jerusalem. The Secret Service says it plans for these types of glitches.
The days before Passover are usually one of the busiest times in Jerusalem, with Israelis swarming stores and supermarkets to get ready. But with Obama in town, downtown Jerusalem was eerily silent.
Well accustomed to the traffic jams caused by visiting world leaders, many residents stayed off the roads, fearing sudden closures, detours and backups.
"The whole city is upside down, we can barely walk and barely drive," said Sophie Casper. "Look at this. It's unbelievable!"
More than 5,000 Israeli police officers were deployed throughout the city, coordinating with American security officials to secure roads for Obama's motorcade, said police spokesman Micky Rosenfeld.
Devora Avidan, a longtime Jerusalem resident, said the streets looked much different than when President Richard Nixon visited Jerusalem in the 1974 the first-ever visit to the city by an American president. Then, Israelis were asked to line the streets to greet the president's motorcade.
Wednesday's scene was more similar to Yom Kippur, she said, the holiest day on the Jewish calendar, when Jerusalem's streets are empty of cars. "It was really nice."
Associated Press writer Daniel Estrin contributed to this report.