Yemen is currently battling Shia Houthi fighters in the north, as well as tackling al-Qaeda fighters based in the country and dealing with a secessionist movement in the south.
Clinton praised the Yemeni government for its efforts to combat al-Qaeda in Yemen, but said it was "time for the international community to make it clear to Yemen that there are expectations and conditions on our continuing support for the government".
International focus has shifted to Yemen in the wake of the attempted bombing of a Detroit-bound aeroplane on Christmas Day.
Al-Qaeda in the Arabian Peninsula claimed responsibility for the attempted attack and Barack Obama, the US president, said that the man accused in the attempt had received his training and explosives in Yemen.
But Clinton's comments have sparked debate over the nature of US intervention in Yemen.
Earlier Abu Baker al-Qirbi, Yemen's foreign minister, made clear that while Yemen was happy to received "development assistance", any military intervention by the US "will counter-fire".
"Yemen is going to deal with terrorism in its own way, out of its own interests and therefore I don't think it will counter-fire," he told Al Jazeera, ahead of Clinton's comments to the media.
Analysts have also warned against direct US intervention in Yemen.
Mark Perry, a Washington-based independent military and foreign policy analyst, said Clinton needed to approach the situation more diplomatically.
"The escalation in the rhetoric seems to have happened overnight," told Al Jazeera.
"Hillary Clinton has looked in her toolbox and pulled out a lecture for the Yemeni government that they have to do something and do something now because a single aeroplane on American tarmac with an unsuccessful bomber has made Yemen an international threat."
He said that while Yemen has become "increasingly destabilised", al-Qaeda, whose affiliate in Yemen al-Qaeda in the Arabian Peninsula, combines both Yemen and Saudi fighters, was far from the major reason for the instability.
"The Houthi rebellion in the north is the key issue here and it can only be solved diplomatically. We're not going to go into Yemen with the 10th Mountain division or the 82nd Airborne and help the Yemenis in their own country. We're only going to destabilise if we do that," he said.
"This is the time for Hillary Clinton to stop lecturing and start working on diplomacy."
Riad Kahwaji, the founder of the Institute for Near East and Gulf Military Analysis in Dubai, said any engagement in Yemen needed to be seen as a long-term strategy.
"You need to turn the environment against them [al-Qaeda], you need to make the environment against their beliefs and ideology"
founder of Institute for Near East and Gulf Military Analysis
"Al-Qaeda in Yemen are Yemenis, they're not foreign fighters ... They have sympathy and support from tribal leaders in parts of Yemen, which is enabling them to move around and function freely," told Al Jazeera.
"You need to turn the environment against them, you need to make the environment against their beliefs and ideology, otherwise military strikes will have very limited results."
Alongside the reopening of the US embassy in Yemen, the British and French embassies, which had also been closed, resumed operations but remained closed to the public, diplomats at those embassies said.
The US embassy said on its website that it was reopening after Yemeni security forces addressed a "specific area of concern".
The statement appeared also to refer to a security operation conducted by Yemeni police Monday in the area of Arhab, 40km north of Sanaa, where two suspected members of al-Qaeda were killed and three others wounded.
Meanwhile, in the US, the attempted Christmas Day bombing incident has prompted a re-evaluation by US officials of its airport security policies.