Mr Coons, a senator for Mr Biden’s home state of Delaware, said he was being told by Republicans they felt they had to toe the line set by Mr Trump and the party leadership.
Only four senators have publicly congratulated Mr Biden - Mitt Romney of Utah, Lisa Murkowski of Alaska, Ben Sasse of Nebraska and Susan Collins of Maine. All of the rest have followed the lead set by Senate majority leader Mitch McConnell, who has said the election remains undetermined until Mr Trump exhausts his legal options.
“My hope is that this is the week when that will begin to turn as it is clear that there is no possible pathway for the president to overturn the results, and we are beginning to threaten the foundations of our democracy, which is a regular, orderly, peaceful transfer of power after every quadrennial election,” he told CNN.
Asked what they were saying in private, he replied: “Bluntly, that they accept - they call me to say congratulations, please convey my well wishes to the president-elect, but I can’t say that publicly yet.”
Far more world leaders have congratulated Mr Biden than Republican senators, with Boris Johnson announcing on Tuesday that he had spoken to the president-elect - one of the first, along with Canada’s Justin Trudeau, to do so.
The leaders of France, Australia, Israel, Spain and Saudi Arabia are among those extending their well-wishes; Emmanuel Macron and Angela Merkel spoke to Mr Biden after Mr Johnson.
Mexico, Russia and China have all held back, saying they were waiting until all legal disputes were concluded - a move designed to pacify Mr Trump in his last 80 days as president.
Mr McConnell on Monday carefully backed Mr Trump, saying that he was “100 per cent within his rights to look into allegations of irregularities,” without citing any evidence or following the president in claiming the election had been stolen.
Mr McConnell’s comments represent the thinking of most Senate Republicans for now, a senior Senate Republican aide told Reuters.
“The position is tenable until it isn’t, and might last for a week or two before it becomes untenable,” the aide said.
The dispute has slowed Mr Biden’s preparations for governing.
A Trump appointee who heads the office charged with recognising election results has yet to do so, preventing the Biden transition team from moving into federal government office space or accessing $9.9 million in funds to hire staff.
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