WASHINGTON/NEW DELHI (Reuters) -U.S. and India trade negotiators were pushing on Wednesday to try to land a tariff-reducing deal ahead of President Donald Trump's July 9 negotiating deadline, but disagreements over U.S. dairy and agriculture remained unresolved, sources familiar with the talks said.

The push comes as Trump announced an agreement with Vietnam that cuts U.S. tariffs on many Vietnamese goods to 20% from his previously threatened 46%. Trump said that U.S. products could enter Vietnam duty free, but details were scant.

Trump threatened a 26% duty on Indian goods as part of his April 2 "Liberation Day" reciprocal tariffs, which were temporarily lowered to 10% to buy time for negotiations.

Sources in India's commerce ministry said that a trade delegation from India was still in Washington a week after arriving for talks that started last Thursday and Friday.

They may stay longer to conclude a deal, but without compromising on key agricultural and dairy issues, the sources said, adding that it was unacceptable to lower tariffs on genetically modified corn, soybeans, rice and wheat grown in the U.S.

Prime Minister Narendra Modi's government "doesn't want to be seen as surrendering the interests of farmers - a strong political group in the country," one of the sources said.

However, India is open to lowering tariffs on walnuts, cranberries and other fruits, along with medical devices, autos and energy products, the source said.

A U.S. source familiar with the talks said that there were "indications that they are close" and negotiators have been told to prepare for a potential announcement.

The source added that "there's been intense and constructive effort to close a deal. I think both sides understand the strategic importance, beyond the economic importance, of closing a deal."

Trump echoed those sentiments on Tuesday, telling reporters on Air Force One that he could reach a deal with India that would cut tariffs for both countries and help American companies compete in India's market of 1.4 billion consumers.

At the same time, Trump cast doubt on a potential deal with Japan, saying he may impose a tariff of 30% or 35% on Japanese goods, well above the 24% duty rate he announced on April 2. Japan is seeking to lower separate 25% automotive and steel tariffs that Trump imposed.

Spokespersons for the U.S. Trade Representative's office, the Commerce Department and the U.S. Treasury did not respond to request for comment on the state of trade negotiations with India and other countries. A spokesperson for India's embassy in Washington did not respond immediately to a request for comment.