Liz Truss and Rishi Sunak have both committed to hosting a reception for the victorious Lionesses at No 10 if they are chosen to be the next prime minister.
Unlike other successful sporting teams, the winning England squad will not be honoured with a visit to Downing Street this week.
Prime Minister Boris Johnson was at the funeral of Northern Ireland peace process architect Lord Trimble on Monday, and is due to go on holiday from Wednesday to Sunday.
Both remaining candidates for Tory leader have now pledged to host the Euro 22 champions at No 10 if they secure the top job.
Foreign Secretary Ms Truss has also promised to ensure the team are “recognised for their historic victory in a suitable way”, amid calls for them to be honoured.
A spokesperson for the Truss campaign said: “The Lionesses have been an inspiration to our nation.
“Liz will host a reception in No 10 if she is prime minister in September and her government would ensure the Lionesses are recognised for their historic victory in a suitable way.”
Mr Sunak’s team said he would also host the Lionesses at Downing Street if made prime minister.
Asked on Monday if Mr Johnson would back damehoods for the team following their win at Wembley, his official spokesman said: “The Prime Minister would definitely want to see the team receive the recognition they rightly deserve for their historic victory.
“On honours specifically, there is obviously a process that is a matter for the independent honours committee, but clearly the public want to see (the) Lionesses receive recognition.”
The England men’s cricket team were invited to Downing Street following their win in the Ashes in 2005, as were the men’s Rugby World Cup victors in 2003.
The women’s national rugby and cricket teams have also previously been honoured with receptions at No 10.
In addition to calling for the Lionesses to receive honours for their Euros win, Labour has urged the Government to capitalise on England’s success to ensure young girls who are now inspired to get playing can go on to become stars.
Lucy Powell, Labour’s shadow secretary of state for digital, culture, media and sport, accused the Tories of having a “terrible record of building on our sports stars’ success with a real and lasting legacy”.
But the Department for Culture, Media and Sport hit back, saying: “We strongly reject these assertions.”
“Ministers continue to promote women’s sport as a top priority and are committed to using the power of the Lionesses’ success to keep pushing to level the playing field,” a spokesperson said.
“We stood by women’s football during the pandemic, with £2.9 million in grants to the Women’s Super League and FA Women’s Championship.
“We put £4.6 million towards the staging of Euro 2022, recently confirmed that the Women’s World Cup and Women’s Euros have been added to the list of events that must be made available to free-to-air television broadcasters, and announced a review of the domestic women’s game that will launch later this summer.
“Right now, we’re investing an extra £230 million into building or upgrading up to 8,000 grassroots facilities by 2025, to ensure we continue to develop the talent of the future and build on the class of 2022’s success.”