Iran Press/America: Senate Majority Leader Mitch McConnell and House Minority Leader Kevin McCarthy both dismissed the idea.
Donald Trump has suggested November's presidential election be postponed, saying increased postal voting could lead to fraud and inaccurate results.
US states want to make mail-in voting easier because of public health concerns over the coronavirus pandemic.
Trump does not have the authority to postpone the election, as any delay would have to be approved by Congress.
Trump's suggestion came as new figures showed the US economy had suffered the worst contraction since the Great Depression of the 1930s.
Donald Trump has suggested November's presidential election be postponed
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Not only, Republicans openly challenge Trump's tweet on delaying the election, but also former President Barack Obama also said that Trump's demand is a grave and imminent threat to American democracy and racial justice.
Senate Judiciary Chairman Lindsey Graham, a South Carolina Republican and Trump ally, said: "I don't think that's a particularly good idea."
Senate Majority Leader Mitch McConnell similarly insisted that the election will go on as planned.
"Never in the history of the country, through wars, depressions, and the Civil War, have we ever not had a federally-scheduled election on time. We'll find a way to do that again this November 3rd," the majority leader said.
Democrats also reacted in the same manner. House Speaker Nancy Pelosi, a California Democrat, responded to the President with a tweet of her own quoting Article II, Section 1 of the Constitution, that gives Congress the authority to "determine the Time of choosing the Electors and the Day on which they shall give their Vote."
House GOP leader Kevin McCarthy of California dismissed Trump's call to delay the election but defended the President's concerns over voting fraud.
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Meanwhile, Any change of date would need to be approved by both houses of Congress - the House of Representatives and the Senate. Democrats control the House of Representatives and some have already said they will not support any delay to the vote.
Any move by Congress to delay the election into 2021 would also require a constitutional amendment, US media quoted constitutional experts as saying.
Earlier this month, six US states were planning to hold "all-mail" ballot elections in November: California, Utah, Hawaii, Colorado, Oregon, and Washington. Other states are considering it, according to a postal voting campaign group.
These states will automatically send postal ballots to all registered voters, which then have to be sent back or dropped off on election day - although some in-person voting is still available in certain limited circumstances.
About half of US states allow any registered voter to cast their ballot by post on request.
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