* Modi to meet Trump in Washington on June 26
* Trade official says visa one of the issues on the table
* Trump's review of U.S. visa programme seen hurting Indian firms
* Trump investigating trade deficit with India (Adds detail)
NEW DELHI, June 20 (Reuters) - Indian Prime Minister Narendra Modi will take up the issue of visas for skilled workers when he meets U.S. President Donald Trump next week in Washington, a senior Indian government official said on Tuesday.
Trump has ordered a review of the U.S. visa programme for bringing high-skilled foreign workers into the United States, putting technology firms and the outsourcing companies that serve them on notice of possible changes ahead.
The review threatens Indian IT services firm such as Infosys Ltd and Tata Consultancy Services which advise large companies on tech issues and carry out a range of tasks for them, relying heavily on the H-1B visa programme.
"The H-1B visa issue will be one of the issues on the table during the PM's visit," Trade Secretary Rita Teaotia told reporters.
Modi will meet Trump in Washington on June 26. The first meeting between them is expected to lay the ground for a further expansion in ties, which grew rapidly under former U.S. President Barack Obama.
However, Trump's focus on building ties with China, coupled with his protectionist trade policies and his characterisation of India as an unscrupulous negotiator in the Paris climate change agreement have raised concern in New Delhi about a drift in relations.
Aside from the visa review, the Trump administration has launched an investigation of countries including India with which the United States runs a bilateral trade deficit.
Teaotia said the government would try to convince Washington that higher exports from India were a win-win for both countries as they helped American companies cut costs and create jobs.
The bilateral trade between the two countries more than doubled to about $115 billion in 2016 from $45.1 billion in 2006. However, the U.S. trade deficit with India also widened.
The trade shortfall was $30.8 billion in 2016, up from $12.7 billion in 2006. (Writing by Rajesh Kumar Singh; Editing by Robert Birsel)