New York  - US President George W Bush Tuesday met with Pakistani President Asif Ali Zardari as the two countries seek to defuse tension over US military strikes in Pakistan.

"Pakistan is an ally, and I look forward to deepening our relationship," Bush said. "Your words have been very strong about Pakistan's sovereign right and sovereign duty to protect your country, and the United States wants to help."

The new Pakistani president who currently wields little political clout both in his own country and abroad, responded: "As always, you prove to the world that your heart is in there for us Pakistanis, we respect your feelings, we respect the American ideals. And we bring to this the whole concept of your promise to the world of bringing democracy to Pakistan."

Zardari, the widower of former prime minister Benazir Bhutto, who was assassinated last year, was sworn in as president earlier this month. His predecessor General Pervez Musharraf, a close US ally in the war against terrorism, resigned after nine years of rule.

"We've got problems. But we will solve them and we will rise to the occasion. That's what my wife's legacy is all about. That's what democracy is all about, to take difficult decisions and do the right thing for the people of our country and our two great nations," Zardari said.

The US has reportedly launched airstrikes in Pakistani territory against Taliban and al-Qaeda militants who seek refuge in the country to launch attacks against US and NATO forces in Afghanistan.

Pakistan's government has accused Washington of violating its territory. US officials have not publicly discussed any operations inside Pakistan but have said the two countries cooperate closely in the war on terrorism.

The US has been frustrated by Pakistan's ineffectiveness at rooting out the militants in the remote tribally governed area along the porous border region.

The two presidents shared a rare, personal moment when Bush spoke about meeting Zardari's children.

"I got to know you a little bit in an interesting way when I met your children at the Olympics.

"And it reminded me about the great suffering that they and you have been through with the loss of your beloved wife. And I thank you very much for staying involved in public service to honor her legacy," Bush said. (dpa)