US Secretary of State Condoleezza Rice has praised progress in the peace process between India and Pakistan.
Ms Rice and Mr Singh discussed "enhanced defence" ties
After meeting Indian Foreign Minister Natwar Singh on the opening leg of her Asian tour, Ms Rice said the US would support the peace process.
She also met Indian PM Manmohan Singh before heading for Pakistan, where she held talks with premier Shaukat Aziz and President Pervez Musharraf.
Ms Rice's eight-day trip will take in six Asian countries.
This is Ms Rice's first visit to the region since she became the top US diplomat in January.
She is due in the Afghan capital, Kabul, on Thursday before returning for further talks in Islamabad the same day.
A state department spokesman said that during three hours of discussions in Islamabad, Condoleezza Rice had expressed her appreciation for what she called Pakistan's superb support in the war on terror.
She also discussed Pakistan's defence and security needs. That included the controversial issue of the sale of F-16 fighter jets to Pakistan.
Earlier in Delhi, she praised what she called "heartening" dialogue between India and Pakistan.
"We very much admire what the Indian prime minister and President Pervez Musharraf have been able to continue, given the change in government here in India," Ms Rice told a joint news conference with Indian Foreign Minister Natwar Singh.
"We want to be supportive in any way that we can."
The foreign minister said he had told Ms Rice that the peace process was "progressing satisfactorily".
The BBC's Jonathan Beale in Delhi says that despite the obvious harmony between the US and India, there are still tensions.
Delhi is worried about the possibility of the US selling F-16 jet fighters to Pakistan, though no decision has yet been made.
Washington is concerned about plans for the construction of a gas pipeline from Iran to India.
Ms Rice said India and the US would look to "enhance defence co-operation".
Natwar Singh said they had discussed "every issue" on defence supplies, "including F16s".
Both said no announcements were going to be made on arms sales.
On the gas pipeline, Ms Rice said: "We have our concerns, but we wish to look at it as a broader problem.
"We do need to look at the broader question of India meeting its energy needs. We believe that a broader energy dialogue should be launched with India."
However, Natwar Singh reiterated India's support for the gas project. "We have no problem of any kind with Iran," he said.
Ms Rice and Natwar Singh also touched on Nepal, saying they agreed to work together to help restore democracy.
Ms Rice said she had a "wonderful" meeting with Sonia Gandhi
Ms Rice said the Nepali government needed get back on a democratic path.
"That simply must happen... it needs to happen very, very soon," she said.
Earlier, Ms Rice had a 30-minute meeting with Congress party president Sonia Gandhi.
During President George W Bush's first term, there was a significant transformation in India-US relations and the US was perceived as a strategic partner.
India and the US have overseen increased military ties, holding joint exercises and expanded civilian, space and hi-tech contacts.
Ms Rice's eight-day trip to South and East Asia will also take her to Pakistan, Afghanistan, Japan, Korea and China.