Washington (CNN) -- U.S. President Barack Obama and Israeli Prime Minister Benjamin Netanyahu repeatedly emphasized the strength and durability of ties between their two countries Tuesday -- part of an effort to dispel the notion that relations between the United States and Israel have frayed in recent months.
They said they had discussed new steps that can be taken to revitalize a Middle East peace process that many observers believe has recently stalled.
The two leaders also took aim at Iran, highlighting common efforts to prevent that country from acquiring a nuclear arsenal.
The meeting -- their fifth since Netanyahu took office last spring -- took place at the White House against a backdrop of speculation that the two leaders are increasingly at odds on a range of key issues.
The "bond between the United States and Israel is unbreakable," Obama told reporters in the Oval Office. The United States remains "unwavering in our commitment to Israel's security".
Reports of damaged relations between Israel and the United States "aren't just premature, they're just flat wrong," Netanyahu insisted.
The two leaders made a point of publicly shaking hands twice, and Netanyahu thanked Obama for offering support in both private talks and public comments.
Obama, however, also stressed the importance of moving toward direct talks between the Israelis and Palestinians. Presently, Netanyahu and Palestinian Authority President Mahmoud Abbas aren't talking directly. They are communicating only through U.S. Middle East envoy George Mitchell, who serves as a go-between for negotiations.
Moving toward direct talks was a topic when Obama met with Abbas on June 9.
"We agreed that, should a progress be achieved, then we would move on to direct talks," Abbas said after that meeting.
Netanyahu said Tuesday that he is ready for direct talks -- a step he has repeatedly endorsed in the past.
Abbas has refused to meet with Netanyahu until Israel promises to stop building settlements. Israel's settlement policy has become point of friction between Israel and the United States.
Relations between Obama and Netanyahu reached a low point in March, when Israel announced plans during a visit by Vice President Joe Biden to construct more than 1,000 new houses in East Jerusalem. The announcement outraged the Obama administration and led to the Palestinians' withdrawing from agreed-upon indirect negotiations with Israel.
In a visit later that month to the United States, Netanyahu was presented with a set of concessions that the White House wanted to see Israel make in an effort to restart the negotiations.
Neither government detailed what the exact nature of the concessions were, but sources on both sides said a halt in East Jerusalem construction was among the demands from the Obama administration.
Also on the agenda: Israel's controversial embargo blocking the flow of goods into Gaza, which turned deadly in May when Israeli forces stormed a vessel that was part of a Gaza-bound humanitarian flotilla. At least nine people were killed.
Obama on Tuesday commended Israel for easing limits on goods going to Gaza, saying there had been "real progress on the ground" that was happening "more quickly and more effectively than many people anticipated".
The president said the United States wants to "ensure the people of Gaza are able to prosper economically while Israel is able to maintain its legitimate security needs in not allowing missiles and weapons to get to Hamas".
Aside from Israeli-Palestinian relations, many Israelis worry about Iran's intentions with its nuclear program. Netanyahu had been expected to urge Obama to keep the pressure on Tehran.
Netanyahu said Tuesday that recent sanctions adopted by United Nations are helping to delegitimize Iran's nuclear program. The sanctions "have teeth" and "bite," he asserted.
