A Number 10 source said any move to extend the franchise would be a bid to "wreck" plans to hold a December election that MPs will vote on tonight.
It came after the SNP's Westminster leader Ian Blackford said his party wants the election age reduced to 16 for all elections and for the franchise to be extended to EU nationals living in the UK.
Mr Blackford told MPs: "I expect the Government today to look positively on any amendments that come forward for EU nationals - there is nothing for the Government to fear by extending the franchise."
Mr Blackford said EU nationals are already on the electoral register as they are allowed to vote in local elections.
But Downing Street said Electoral Commission guidance said any changes to the franchise should be made at least six months before an election. A Number 10 source said a last-minute change to electoral rules would risk the legitimacy of any poll.
Downing Street said votes for EU nationals could cause "administrative chaos" while allowing 16 and 17-year-olds to take part would be "administratively impossible" to deliver.
"There are long-standing conventions that election laws should only be changed after appropriate consultation," the Prime Minister's spokesman said.
"The Electoral Commission warns against changing electoral laws less than six months before an election."
Deputy Commons speaker Lindsay Hoyle must rule whether changes to the franchise are within the scope of the one-line bill calling an early election.
Putting forward the legislation, Boris Johnson accused MPs of trying to delay Brexit "forever".
The Prime Minister said a "new and revitalised" Parliament was needed to take Britain out of the European Union as he introduced legislation for a poll on December 12.
Mr Johnson took aim at Labour leader Jeremy Corbyn's previous opposition to an election, and claimed Labour was not interested in delivering Brexit.
"All they want to do is procrastinate," he told the Commons.
"They don't want to deliver Brexit on October 31, on November 31, even on January 31."
He added: "They just want to spin it out forever, until the 12th of never. And when the 12th of never eventually comes around, they'll devise one of their complicated parliamentary procedures and move a motion for a further delay and a further extension then."
Mr Corbyn said his party “backs a general election because we want this country to be rid of this reckless and destructive Conservative Government."
"Today, after much denial and much bluster by the Prime Minister, that deal is officially off the table.
"So this country can vote for the Government that it deserves."