Mr Jones told BBC Radio Wales it was the prime minister's "constitutional duty" to seek the Queen's permission to form a government, and defended her choice of partners.
Theresa May has admitted she "wanted a different result" in the General Election but insists the Conservatives are the "only party" in a position to form a government and lead Brexit talks. MP Anna Soubry called on May to "consider her position" following "a pretty terrible campaign", in which the Conservatives squandered much of a 20-point lead in the polls.
"Clearly if she's got a worse result than two years ago and is nearly unable to form a government, then she, I doubt, will survive in the long term as Conservative Party leader", former Conservative Treasury chief George Osborne said on ITV. Buoyed by strong polling numbers, May and her party were confident of a landslide victory.
This was an issue we covered on MNN just before the American election where I wrote that Grumpy boomers may have won it, but millennials failed to show up.
SNP leader Nicola Sturgeon, who has headed the party since 2014, said that the poor results meant that she would need to "reflect" on the appetite for a new referendum.
Meanwhile, the opposition Labour Party, led by Jeremy Corbyn, picked up 29 seats in Parliament.
Mrs May initially built the whole election campaign around her own personal brand - often dropping the word Conservatives from leaflets and posters.
The Conservatives, as the largest party, have the best chance of achieving this, especially with the support of the Democratic Unionist Party, a natural ally. The biggest loser of the night was the United Kingdom Independence Party (UKIP), which was all but decimated, as its voters flocked en masse to both Labour and Conservatives.
May spent the campaign denouncing Corbyn as the weak leader of a spendthrift party that would crash Britain's economy and flounder in Brexit talks, while she would provide "strong and stable leadership" to clinch a good deal for Britain.
May to form government with help of Democratic Unionist party
The fear in Belfast is that a close working relationship between May's government and the DUP could affect the devolution crisis. Some Tories are publicly - and undoubtedly many privately - suggesting her days as prime minister and party leader are numbered.
Dogus sharply closed the gap on the sitting member of parliament from Prime Minister Theresa May's Conservatives in the Cities of London and Westminster constituency - home to Buckingham Palace, the Houses of Parliament and the British capital's financial centre.
She was criticized for a lacklustre campaigning style and for a plan to force elderly people to pay more for their care, a proposal her opponents dubbed the "dementia tax".
Combined, the Conservatives and the DUP would have 329 MPs in the Commons.
With a hung parliament guaranteed, the so-called "hard Brexit" that May had been pushing for seems less and less likely to pass. Her predecessor, David Cameron, first asked British voters to decide in 2016 whether to leave the EU.
"This government will guide our country through Brexit talks".
"What tonight is about is the rejection of Theresa May's version of extreme Brexit", said Keir Starmer, Labour's policy chief on Brexit, Reuters reported.
European Union leaders fear May's loss of majority raises the risk of failure in Brexit negotiations due to start this month that will usher Britain out of the EU in March 2019.
One of the lead European Union negotiators, Guy Verhofstadt, criticized May on Twitter, writing: "Yet another own goal, after Cameron now May, will make already complex negotiations even more complicated".
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