India and the US have made "significant progress" on a number of trade-related issues, and both the countries are "optimistic" of reaching a kind of trade agreement in the near future. US President Donald Trump said his country will soon have a trade deal with India.

"I think very soon. We are doing very well. (US Trade Representative) Robert Lighthizer who is right here negotiating with India... I think, very soon we will have a trade deal," Trump told reporters when asked if there is any trade deal is expected between India and the US.

"We will have a larger deal down the road ... but we will have a trade deal," Trump added. However, no timeline was given by either side regarding finalisation of the deal.

Prime Minister Narendra Modi met Trump on the sidelines of the UN General Assembly session and discussed with him bilateral ties.

The two countries are negotiating a trade package to iron out bilateral trade issues and promote the two-way commerce. The US has been pressuring India to lower duties on its products and address the trade deficit.

Speaking at the press conference, Modi said: "As far as trade is concerned, I am very happy that in Houston, in my presence there was an agreement signed by Indian company Petronet for USD 2.5 billion, which is the amount of investment the Indian company is going to do in the energy sector and this will mean that in the years to come, this will result in trade of an amount of $60 billion and create 50,000 jobs which I think is a big initiative taken by India."

The Petronet deal, the largest by an Indian company in US LNG, came after Modi had a meeting with the CEOs of top US-based oil companies on Saturday last week.

Addressing media after the meeting of the two leaders, Foreign Secretary Vijay Gokhale said that there was no discussion on timeline, but "we are optimistic that we will be able to conclude an understanding or an agreement fairly soon".

Gokhale rejected claims that a trade deal between the US and India has derailed, saying such an assumption is “completely off the track.” He said it would a completely wrong interpretation to say this as significant progress has been made at the trade deal front.

"These are issues which are complex. These issues involved industries of both the sides. It involves jobs on both sides," he told reporters. The secretary said that reconciling the 'gives and takes' in a deal require certain amount of discussions and balance.

"We have made significant progress in that regard, and we are quite confident that we will make further progress in the future," he added.

The USTR and India's Commerce and Industry Minister Piyush Goyal, who rushed to New York from Dubai, have expressed satisfaction on their discussions.

"I would certainly think that the discussions that have taken place in New York over the last two weeks are precisely the opposite (of the term trade deal derailed)," Gokhale said.

When asked about the details, the secretary said India is expecting it to be a "fair and reasonable" deal and "we have laid out our requirements in that regard, so is the US side".

It is now a matter of negotiations between the two sides on individual issues, he said, adding that at the same time, "we also address the US side concerns regarding what they considered to be a trade deficit".

India and the US have made significant progress in terms of growing trade in the last three-four years and reducing trade deficit.

"Both the leaders (the Indian Prime Minister and US President) reviewed the discussions that are ongoing," he said adding "we have narrowed the areas of difference".

"The two leaders, therefore, felt that they were optimistic in terms of us reaching some kind of a trade agreement in near future and discussions will continue in this regard," he said.

There are expectations of announcement of a trade deal or package during the Prime Minister's visit.

India is demanding exemption from high duties imposed by the US on certain steel and aluminium products, resumption of export benefits to certain domestic products under their Generalised System of Preferences (GSP), greater market access for its products from sectors, including agriculture, automobile, auto components and engineering.

On the other hand, the US wants greater market access for its farm and manufacturing products, dairy items and medical devices, and cut on import duties on some ICT products. The US has also raised concerns over high trade deficit with India.

In 2018-19, India's exports to the US stood at $52.4 billion, while imports were $35.5 billion. Trade deficit dipped from $21.3 billion in 2017-18 to $16.9 billion in 2018-19.

India received FDI worth $3.13 billion from the US in 2018-19, higher than $2 billion in 2017-18.