The dispute has seen Poland and Hungary block 1.8 trillion euros (1.61 trillion pounds) worth of EU funds, including hundreds of billions due to be disbursed soon to help pull the bloc out of a double-dip recession caused by a second wave of COVID-19.
"I... reaffirmed our readiness to veto the new budget if we do not find a solution that is good for the EU as a whole, not just for some of its members," Morawiecki wrote on his Facebook page.
The European Union is currently investigating the nationalist governments of Poland and Hungary for undermining the independence of their judiciaries and media. Brussels has sought to attach conditions to the disbursement of EU cash.
"Today I told the (German) chancellor that Poland expects further work to find a solution as soon as possible that would guarantee the rights of all Member States and respect treaty procedures," Morawiecki wrote.
On Thursday he held talks in Budapest with Hungarian Prime Minister Viktor Orban. The two allies issued a joint declaration saying the EU could not attach rule-of-law conditions to funds unless the bloc changed its founding treaty.
Polish government spokesman Piotr Muller told state-run news agency PAP on Friday Morawiecki had sent European Commission President Ursula von der Leyen a second letter concerning the attempt to link the funds to rule-of-law concerns.
(Reporting by Alan Charlish and Pawel Florkiewicz; Editing by Gareth Jones)