"The ASEAN countries need to hold the regime accountable for that ... continue to demand the cessation of violence and release of prisoners," he added.
ASEAN's nine members and Myanmar junta chief Min Aung Hlaing in April last year signed an agreement that included immediate cessation of violence and dialogue among all parties.
"There has been no positive movement on that."
Myanmar's military has increased pressure against ethnic minority armies since a coup last year and is encountering resistance on multiple fronts, including militia groups allied with the ousted government.
Last week, Thailand scrambled fighters after Myanmar jet breached its airspace in the country's northwest.
Myanmar shares a 2,400-km (1,500-mile) border with Thailand, its longest with any neighbour.
The United States and Thailand on Sunday signed agreements to deepen the countries' already strong ties as Washington steps up its efforts to counter China's expanding influence in Asia.
Blinken's visit comes a day after he met Chinese foreign minister Wang Yi in Indonesia on the sidelines of the G20 foreign minister's meeting.
China's Wang has been engaged in intense diplomacy across Asia in recent weeks and met Thai Prime Minister Prayuth Chan-ocha on Tuesday.
Blinken last year postponed a trip to Thailand, the oldest U.S. ally in Asia, after halting a regional tour when a COVID-19 case was found in the press corps accompanying him.
After meeting Blinken, Prayuth said the relationship between the two countries "continue to increase in momentum."
The Biden administration has sought to shore up ties with a region that had become uncertain about U.S. commitment during a period of perceived neglect under Biden's predecessor, Donald Trump. At that time, China expanded its influence while pushing investment and trade integration.
After Thailand, he will make a previously unscheduled stop in Tokyo to offer condolences to the Japanese people after the killing of former Prime Minister Shinzo Abe, the State Department said.