Bavarian state premier Horst Seehofer said he would send the federal government a written request within the next two weeks to restore "orderly conditions" at the nation's borders, through which one million migrants and refugees passed last year alone.
"If it doesn't follow, the state government will have no other choice but to file a suit at the federal constitutional court," Seehofer told Der Spiegel magazine.
Seehofer has issued a series of ultimatums to Merkel in recent months to press her into taking immediate action to limit the influx of migrants, only to back down at the last minute.
His comments reflect increasing doubt among Germans about Merkel's "we can do this" mantra in the face of Europe's biggest migrant crisis since World War Two, especially since assaults in Cologne on New Year's Eve were blamed on migrants.
Merkel's popularity has dropped following the assaults, a poll showed Friday.
Bavaria, a conservative state that borders Austria to the south, is the home of Seehofer's Christian Social Union (CSU) -- sister party to Merkel's Christian Democratic Union (CDU) -- and is the main entry point for migrants and refugees.
The state's finance minister, Markus Soeder, told Der Spiegel Merkel's refugee policy was not democratically legitimised and said parliament should vote on the matter, Reuters reported.
Senior figures from the Social Democrats (SPD), Merkel's second coalition partner, have also broken ranks in recent days by challenging her welcoming approach to asylum seekers.
SPD leader Sigmar Gabriel joined the critical voices Saturday. "We have to get from a chaotic to an orderly immigration," he told several regional newspapers.
He said border checks needed to be improved and refugee quotas should be introduced to maintain control over how many people come to Germany and when they arrive.
Germany could take in more than the 200,000 refugees proposed by Seehofer as an official cap for this year, Gabriel said. "But the quota also has to be significantly below the immigration numbers of the previous year," he added, without giving a concrete figure.