Kashmir is divided between the South Asian rivals, but both claim the Himalayan region in full and have fought two wars over it.
"I will use my trip to urge the leadership to continue solving this issue with the idea that it can be solved," Bush told state-owned Pakistan Television in an interview in Washington, broadcast on Sunday.
He said his discussions with General Pervez Musharraf, his Pakistani counterpart, and Manmohan Singh, the Indian prime minister, revealed that attitudes had changed since he first came to office in 2000.
In 2002, the nuclear neighbours came close to war, but in the past two years they have pursued peace talks.
"I believe a lasting solution can be achieved... I've seen the progress that's been made in the relations since I first became president"
"I believe a lasting solution can be achieved," Bush said. "I've seen the progress that's been made in the relations since I first became president."
Pakistan has become a valuable ally of the US in the "war on terror".
Bush said he wanted to use his trip to Islamabad next Saturday to let Pakistanis know "that the American people care about them".
"This is a relationship that's much bigger than the war on terror," said Bush, referring to the American relief response to the 8 October earthquake that devastated Pakistan-administered Kashmir.
Bush said "we'll be talking about a bilateral investment treaty" as a step towards increasing trade between the US and Pakistan, and student exchange programmes.