The Left on Saturday appeared ready to give the UPA time to respond to its suggestions, but equally ready to snap the government's lifeline if it did not find the responses satisfactory.
"It is for the Congress leadership to decide on the matter which will have serious consequences for the government and the country," a CPM politburo resolution said.
A politburo member said: "The message is very clear. We have warned the government about serious consequences if it proceeds with it. What does serious consequence mean? We cannot support the deal. And the US has clearly said that the deal will not be renegotiated."
CPM General Secretary Prakash Karat said: "(Negotiations with IAEA) should not be taken up now. The government knows majority in Parliament are not in favour of the deal. We have met Prime Minister Manmohan Singh and Congress President Sonia Gandhi and explained our views and how it was necessary to pause and review (the agreement)."
Politburo member Sitaram Yechury and External Affairs Minister Pranab Mukherjee were also present at the meeting.
A meeting of the CPM central committee has been convened on August 22 and 23. A meeting of the four Left parties will be held in the next few days.
D Raja of the CPI said the Left's level of cooperation with the Congress-led coalition will "go down from now on" and it would be a "merit-based support".