On Saturday, Mr. Dodon’s Russian-backed Socialist Party announced that it was forming a coalition government with a rival bloc, A.C.U.M., which favors greater cooperation with the European Union. That unlikely alliance was intended to keep the Democratic Party of Moldova, run by the tycoon Vladimir Plahotniuc, out of power.

The Democratic Party, to which Mr. Filip also belongs, said that the new administration had tried to usurp power at Russia’s behest and criticized Mr. Dodon’s refusal to dissolve Parliament after the parties missed a court-mandated June 7 deadline to form a government.

Thousands of supporters of the Democratic Party rallied in the capital, Chisinau.

Denouncing the decision to remove him from the presidency, Mr. Dodon said the court was not politically independent and accused the Democratic Party of trying to cling to power. He called on the international community to step in.

“Moldovan citizens with different views on domestic and foreign policy can unite for the sake of a common goal: liberation of the Republic of Moldova from the criminal, dictatorial regime,” Mr. Dodon said in a statement.

“In this situation, we have no choice but to appeal to the international community to mediate in the process of a peaceful transfer of power,” he added, urging Moldovans to take part in “an unprecedented mobilization and peaceful protests.”