ATHENS — With Greece in the final stretch of negotiations with its creditors, aimed at unlocking rescue loans the country needs to avert an imminent default, Prime Minister Alexis Tsipras faces growing pressure from the ranks of his own party.

After weeks of simmering dissent among the more radical elements of his leftist Syriza party, Mr. Tsipras on Sunday faced his biggest challenge from within the party since taking office in January. A faction known as the Left Platform proposed that Greece stop paying its creditors if they continue with “blackmailing tactics” and instead seek “an alternative plan” for the debt-racked country.

The proposal came as the interior minister, Nikos Voutsis, told Greek television that Athens would not be able to make debt repayments of 1.6 billion euros, or nearly $1.8 billion, that are due next month to the International Monetary Fund, one of Greece’s three international creditors.

“The money won’t be given,” Mr. Voutsis said. “It isn’t there to be given.”

The proposal by the Left Platform, which is led by Panagiotis Lafazanis, the energy minister, and represents around 30 of Syriza’s 149 representatives in the Greek Parliament, was rejected by the party’s central committee late Sunday by a vote of 95 to 75.