In the occupied West Bank, Palestinian security sources said Israeli troops killed a member of Islamic Jihad and a fighter allied to Fatah.
The Israeli military said it arrested 15 wanted Palestinians overnight during operations across the West Bank.
Meanwhile, Ehud Barak, the new Israeli defence minister, has ordered the army to allow wounded Palestinians stranded on the Gaza Strip border to enter Israel for medical treatment.
"Barak on Wednesday ordered the army and co-ordinator of Israeli activities in the Gaza Strip to provide emergency medical assistance in Israeli hospitals to wounded Palestinians blocked at the Erez crossing," a spokeswoman said.
On Tuesday, the military authorised Israeli ambulances to evacuate five Palestinians, including two trapped at the Erez crossing - the main border crossing for people between Gaza and Israel - to hospitals in Israel.
Agencies said on Wednesday that Israeli army tanks and troops penetrated several hundred metres into the Gaza Strip in an overnight raid.
An Israeli soldier was wounded by gunfire from Palestinian fighters during Wednesday's early morning raid near the Kissufim border crossing, an army spokesman said.
"Hamas must decide what their objective is - is it power, is it Israel's destruction, or is it peace for the Palestinian people?
Chris, Stockholm, Sweden
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Wednesday's raid comes a day after Israeli tanks crossed into Gaza near the Erez (Beit Hanoun) crossing point, where hundreds of Palestinian civilians were trapped after attempting to leave the territory.
An Israeli army bulldozer was seen knocking down concrete barriers at the crossing and shots were fired from the Israeli side of the border.
Palestinians trapped at Erez, many of them Fatah supporters, are attempting to leave Gaza for the West Bank or Israel after Hamas's takeover last week.
Some Palestinians said they had been trapped at the crossing for five days.
In Tuesday's other develpments, the US president and Israeli prime minister in Washington pledged their support to the new Palestinian emergency government.
The emergency government, headed by Salam Fayyad, was formed on the orders of Mahmoud Abbas, the Palestinian president and leader of Fatah, after Hamas fighters took control of Gaza last week.
George Bush and Ehud Olmert said they were committed to the creation of a Palestinian state next to a secure Israel during a meeting in Washington.
The two leaders have sought to further isolate Hamas militarily, financially and diplomatically following its Gaza takeover.
Fatah continues to maintain security control in the larger West Bank territory.