Reports say at least two Palestinians have also been killed.

Israel says the fighting started when its troops crossed into Gaza after spotting militants planting explosives along the border.

Reports from inside Gaza say the militants then tried to capture an Israeli soldier.

Retaliation

The BBC's Jon Donnison, in the West Bank city of Ramallah, says many inside Gaza will now expect retaliation from Israel to be stepped up following the deaths of the soldiers.

The army said an officer and a conscript died when gunmen fired on a military patrol inside the Gaza Stip. Two soldiers were injured and two Palestinian fighters killed in the clash, it said.

The two soldiers killed were named by Israel's Haaretz newspaper as Eliraz Peretz, 31, and 21-year-old Ilan Sebiatkovsky.

Army spokeswoman Avital Leibovich described their deaths as "tragic" and "painful".

"I think it's true to say that this is one of the fiercest days we have had since operation Cast Lead happened," she said, referring to the Israeli offensive.

A ceasefire between Israel and Islamist militant group Hamas, which governs Gaza, has largely held since the Israeli offensive.

However, hundreds of rockets have been fired into southern Israel by militants in Gaza.

Hamas's armed wing - the al-Qassam Brigades - said in a statement sent to the BBC that it had killed the two soldiers.

Speaking to Reuters news agency, Hamas spokesman Abu Obeida is quoted as saying: "This was our work, but was carried out for defence."

Militants have been holding another Israeli soldier, Gilad Shalit, for more than three years.