"The program for Greece is the least difficult of all the difficult alternatives. The problems it addresses are real," he warned.
Merkel and Barroso spoke after Greeks withdrew hundreds of millions of euros from banks, prompting the president of Greece's central bank to warn that panic is possible, but is not taking place.
Greeks pulled about 800 million euros out of the banking system Monday, President Karolos Papoulias said.
He said he had spoken to Central Bank Governor George Provopoulos about it.
"There is, of course, no panic, but there is fear that could develop into panic," Papoulias said, describing what the bank governor told him. "He also said that the strength of banks is very weak at the moment."
The Greek debt crisis threatens the stability of the European Union's single currency.
Europe is worried that Greece could fail to make debt payments as early as next month, which could force the country out of the euro.
Merkel said she is working to keep Greece in the eurozone, but she refused to be drawn into talk about what would happen if Greece did not meet its debt obligations.
The head of the European Central Bank echoed Merkel's remarks.
"I want to state that our strong preference is that Greece will continue to stay in the euro area," Mario Draghi said in a speech in Frankfurt on Wednesday.
The European Central Bank and International Monetary Fund have been pumping money into Greece to keep the country in the euro, but they have demanded that the Greek government slash spending to get the funds.
Radical leftist leader Alexis Tsipras, whose Syriza party reaped the benefits of voter frustration with the austerity measures, urged Greeks on Tuesday to continue resisting "the parties of the bailout."
"They asked us to leave the country without any hope," he said, arguing that the May 6 election had made the terms of the bailout "null and void."
New Democracy leader Antonis Samaras, meanwhile, said his party will "keep fighting for a developing Greece within Europe" and "against those who say they want to get Greece out of Europe."
His party narrowly came in first in the May 6 elections, but opinion polls since then have suggested that Syriza would finish in first place in a new election.