Of the six F-16 fighter jets that Thailand readied to deploy along the disputed border, one of the aircraft fired into Cambodia and destroyed a military target, the Thai army said.
Both countries accused each other of starting the clash early on Thursday.
"We have used air power against military targets as planned," Thai army deputy spokesperson Richa Suksuwanon told reporters.
Thailand also closed its border with Cambodia.
Cambodia's defence ministry said the jets dropped two bombs on a road, and accused its neighbour of opening fire on its troops and violating an agreement designed to de-escalate tension.
The skirmishes came after Thailand recalled its ambassador to Cambodia late on Wednesday and said it would expel Cambodia's envoy in Bangkok, after a second Thai soldier in the space of a week lost a limb to a landmine that Bangkok alleged had been laid recently in the disputed area.
Thai residents in the Surin border province fled to shelters built of concrete and fortified with sandbags and car tires as the two countries exchanged fire.
"How many rounds have been fired? It's countless," an unidentified woman told the Thai Public Broadcasting Service (TPBS) while hiding in the shelter with gunfire and explosions heard intermittently in the background.
For more than a century, Thailand and Cambodia have contested sovereignty at various undemarcated points along their 817km land border, which has led to skirmishes over several years and at least a dozen deaths, including during a week-long exchange of artillery in 2011.
Tensions were reignited in May following the killing of a Cambodian soldier during a brief exchange of gunfire, which escalated into a full-blown diplomatic crisis and now has triggered armed clashes.
The clashes began early on Thursday near the disputed Ta Moan Thom temple along the eastern border between Cambodia and Thailand, around 360km from the Thai capital Bangkok.
"Artillery shell fell on people's homes," Sutthirot Charoenthanasak, district chief of Kabcheing in Surin province, told Reuters, describing the firing by the Cambodian side.
"Two people have died," he said, adding that district authorities had evacuated 40,000 civilians from 86 villages near the border to safer locations.
Thailand's military said Cambodia deployed a surveillance drone before sending troops with heavy weapons to an area near the temple.
Cambodian troops opened fire and two Thai soldiers were wounded, a Thai army spokesperson said, adding Cambodia had used multiple weapons, including rocket launchers.
A spokesperson for Cambodia's defence ministry, however, said there had been an unprovoked incursion by Thai troops and Cambodian forces had responded in self-defence.
Thailand's acting Prime Minister Phumtham Wechayachai said the situation was delicate.
"We have to be careful," he told reporters. "We will follow international law."
An attempt by Thai premier Paetongtarn Shinawatra to resolve the recent tensions via a call with Cambodia's influential former prime minister Hun Sen, the contents of which were leaked, kicked off a political storm in Thailand, leading to her suspension by a court.
with AP
9°C