Following the victory of Pedro Sánchez in Sunday's Socialist Party (PSOE) leadership contest, Podemos has offered to withdraw a motion of no confidence against Mariano Rajoy that it tabled last Friday, if the new socialist leader is prepared to present a motion of his own.
Podemos' organisation secretary, Pablo Echenique, said his party was ready to make the move "if they understand they need to present a PSOE motion, we would withdraw ours".
Earlier on Monday morning, PSOE MP Meritxell Batet, considered to be close to Mr. Sánchez, said during a radio interview that Podemos should withdraw their motion of no confidence "if they really want to change the prime minister and get rid of Rajoy".
"When a motion is presented, first the work must have been done with other groups to try to make it a success, otherwise it's merely symbolic and about showing off. The most sensible thing to do would be to withdraw it."
The Spanish Constitution requires the party that tables a motion of no confidence to propose a new candidate for Prime Minister as part of the motion.
The seven-page version presented by Podemos on Friday named Pablo Iglesias as the alternate candidate and said the main reasons behind the motion were related to a range of corruption scandals that have engulfed the Popular Party (PP).
Shortly before Podemos made its announcement on Monday, Spanish Prime Minister Mariano Rajoy ruled out an early general election following Mr. Sánchez's victory.
"There will be no early elections", he said.
"Do not count on me to generate instability in Spain: my bet is on being sensible, and we will continue to seek agreements."
He said he had not phoned Mr. Sánchez to congratulate him "so as not to bother him".
A joint PSOE-Podemos motion of no confidence would fall 20 seats short of the 176-seat majority needed to oust Mr. Rajoy, so the two left-wing parties would have to seek the support of regional nationalists in Catalonia and the Basque Country.