The Queen's Speech is written by the government and presents an outline of its planned legislation for the next Parliamentary session.
The Queen's Speech is read by the Queen from the Throne in the House of Lords at the State Opening of Parliament.
The set-piece event had been due to take place next Monday with the 91-year-old Queen Elizabeth II delivering the address.
Brexit Secretary David Davis predicted some parts of the Tory manifesto would now have to be "pruned" after the Tories lost their Commons majority.
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The BBC reported that the decision to delay it revealed an "ambiguity" about what would go in it - with several manifesto pledges expected to be watered down or dropped - but also the need for the Tories to "nail down" DUP support.
A defeat for its Queen's Speech would be tantamount to a vote of no confidence in the new minority government, it said.
Any delay in the Queen's speech would be difficult to accommodate, given the monarch is scheduled to attend Royal Ascot from next Tuesday until the end of next week, The Guardian reported.
There has already been one major change to the royal diary because of the Queen's speech: the Order of the Garter service was cancelled to accommodate the June 19 date at short notice.
The Conservatives went from 331 seats to 318 in the general election, while Labour increased its number of MPs from 232 to 262.
They are expected to raise concerns about her leadership style, and press for more details on talks with the DUP.
May's new Cabinet will also meet for the first time after a reshuffle.
Speaking to BBC Radio, Davis said that while the Tory election campaign had been disappointing, May was a "formidable prime minister" and accused people speculating about her leadership of "the absolute height of self- indulgence".
The PM finalised her cabinet with a small reshuffle, with Michael Gove returning to a ministerial role as environment secretary.
A number of high-profile members kept their posts in yesterday's Cabinet reshuffle, with Philip Hammond staying at the Treasury, Boris Johnson remaining at the Foreign Office, Amber Rudd keeping the Home Office brief and Priti Patel remained the senior-most Indian-origin Cabinet minister, holding on to her position as the secretary of state for international development.