NEW YORK - President George W Bush Tuesday reaffirmed United States' respect for Pakistan 's sovereignty at his talks with President Asif Ali Zardari aimed at defusing tension over US military strikes in the Pakistani territory. But the US leader did not give any categorical assurance that such violations would not take place in future. "President Bush said we are alive to Pakistan 's concerns about its sovereignty and we respect its sovereignty and territorial integrity," Information Minister Sherry Rahman told reporters at a briefing following half-an-hour meeting between the two leaders on the margins of the UN General Assembly. She did not elaborate whether this meant that there would be no more cross-border raids. At the start of the meeting, Bush said, "Pakistan is an ally, and I look forward to deepening our relationship. 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." Bush pledged continued support for Pakistan in economic and security fields. The two leaders met with their full delegations for 10 minutes followed by one-on-one talks for another 20 minutes. The discussions covered a wide range of issues including democracy, economic development and counter-terrorism with the two leaders establishing a good rapport in their first-ever talks, said the minister, who was a member of the Pakistani side at the meeting. "President Bush praised President Zardari's courage and commitment to fight off terrorism despite his great personal loss," and acknowledged that he had stood up to the challenges, Sherry added. The US leader lauded Pakistan 's important role in the fight against terrorism. Bush also expressed Washington's full support for Pakistan 's initiative towards holding a conference - Friends of Pakistan - to drum up international support for its economic development. It was noted in the discussion that Pakistan-US strategic relationship would not be confined to security issues alone but cover wide-ranging areas like socio-economic development, agriculture and education. Bush expressed condolences for the friends and relatives of the more than 50 people killed and hundreds others who were wounded in the Marriott bombing on Saturday that rocked the nation. "I know that you, your heart went out to the families of those who suffer and so does the collective heart of the American people," Bush said. "We stand with you." Bush recalled meeting Zardari's children this summer at the Olympics in Beijing. "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 honour her legacy," Bush said. Zardari said democracy is the answer for Pakistan . "We will solve all the problems. We have a situation. We have issues. We've got problems. But we will solve them and we will rise to the occasion," Zardari said. "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. We should come together in this hard time and we will share the burden and the responsibility with the world." President Zardari thanked the US for its support for the restoration of democracy in Pakistan and was confident that Pakistan would be able to overcome problems confronting it. "It's been the help of all the friends around the world and we are thankful to the world for helping democracy," Zardari said. The Pakistani delegation included Foreign Minister Shah Mehmood Qureshi, Finance Minister Naveed Qamar, Information Minister Sherry Rahman, National Security Adviser to Prime Minister Mahmud Ali Durrani and Pakistan 's Ambassador to the United States Husain Haqqani. The US side included Secretary of State Condoleezza Rice, National Security Adviser Stephen Hadley and Assistant Secretary of State for South Asia Richard Boucher.