Pawlenty, who became the first top-flight Republican to form a presidential exploratory committee last week, said that he supported the U.S. airstrikes against the Libyan dictator, but would have acted sooner when rebel forces had "substantial momentum."
"Now we're in this position of having the president of the United States saying Kadafi must go, but we're not going to necessarily make him go. And that's untenable," he said.
Pawlenty's comments, in an interview on MSNBC's "Morning Joe," stand out because most of the other Republicans considered likely to seek the party's nomination have yet to respond to the president's speech Monday night.
There is a danger for would-be candidates seeking to match a uniquely presidential moment like Monday, a nationally televised address from the nation's commander in chief. The volatility of events in the Middle East and North Africa offer a particular challenge for a field without a clear foreign policy heavyweight.
Newt Gingrich, who is raising funds in anticipation of a presidential campaign, has been criticized for his seemingly contradictory positions regarding the situation in Libya. A spokesman said he was traveling Monday and would not be responding to Obama.
In his interview, Pawlenty did not seek to specifically rebut Obama's speech but offered a broader critique of his foreign policy.
"For the leader of the free world, the United States of America, it's not appropriate to be sitting on the sidelines and just watch history unfold without exerting some leadership," he said, later faulting Obama for the "subordination of American interests and power to the Arab League and the United Nations."
The party's last nominee has been more outspoken in reacting to the president's address.
On Fox News Channel on Tuesday, Sen. John McCain (R-Ariz.) called Obama's hesitance to advocate for regime change "incomprehensible."
"He obviously doesn't understand that if we don't overthrow Kadafi, we risk a stalemate," he said.
For his part, Obama will continue making his case Tuesday during a series of interviews with network anchors in New York, where he also is speaking at the dedication of the new United States mission to the United Nations.