Israel has rejected a deadline by Palestinian militants believed to be holding an Israeli soldier in Gaza to begin freeing Palestinian prisoners.
Israel has threatened to intensify its actions in Gaza
Militants gave Israel until 0300 GMT on Tuesday to release some 1,500 prisoners or face unspecified "consequences".
But Israeli PM Ehud Olmert said he would not give in to "extortion".
Palestinians said missiles hit Gaza twice early on Tuesday, killing one militant in northern Gaza and striking the Islamic University in Gaza City.
The first strike, shortly after midnight (2100 GMT), killed one militant and injured another in the town of Beit Lahiya, Palestinian sources said.
The Israeli army said the men had been planting explosives in an area close to its forces.
SOLDIER CAPTURE TIMELINE
Sun 25 June: Cpl Gilad Shalit captured in cross-border attack
Mon 26 June: Palestinian Popular Resistance Committees demand prisoner releases in exchange for Shalit
Weds 28 June: Israeli military enters southern strip after launching air strikes on Gaza
Thurs 29 June: Israel detains dozens of Hamas officials
Sat 1 July: Groups believed to be holding Cpl Shalit demand 1,000 prisoners be released
Mon 3 July: Groups holding soldier issue ultimatum for 0300 4 July
Two hours later a missile strike on Gaza City hit a building of the university, a stronghold of the Hamas group, Palestinians said.
The night-time strikes came after Israeli artillery pounded northern Gaza on Monday and a small force entered the area for the first time since Israel began its assault last Tuesday night.
Israeli aircraft also hit more targets across Gaza, and two militants were reported killed. Eight militants have now died since the start of the offensive.
In a statement, the three groups believed to be holding Cpl Gilad Shalit set a deadline for Israel to start releasing prisoners.
"We give the Zionist enemy until 0600 [0300 GMT] tomorrow, Tuesday 4 July."
If Israel does not meet their demands the groups "will consider the soldier's case to be closed", the statement said.
"The enemy must bear all the consequences of the future results," it concluded.
The militant groups have demanded that all Palestinian women and young prisoners be released along with 1,000 male prisoners in exchange for information about Cpl Shalit's welfare.
The BBC's Katya Adler in Gaza City says the groups did not specify what action they would take, but, she says, Israelis will worry it may mean their soldier will be killed.
However Israel swiftly dismissed the ultimatum.
"The government of Israel will not yield to the extortion of the Palestinian Authority [PA] and the Hamas government, which are led by murderous terrorist organisations," Prime Minister Olmert's office said.
"We will not conduct any negotiations on a prisoner release."
The Hamas-led PA has denied knowledge of the whereabouts of Cpl Shalit, who was captured in a cross-border raid eight days ago.
Two other soldiers and two attackers died in the ambush.
Hamas' Izzedine al-Qassam Brigades, the Popular Resistance Committees and the little-known Islamic Army say they are holding the 19-year-old tank gunner.
Mr Olmert says Israel's army has been authorised to do whatever it takes to get Cpl Shalit back.
In other developments, Israeli troops were reported to have seized at least two Palestinians early on Tuesday from a police station in the West Bank city of Ramallah, where they were being held on suspicion of killing a Jewish settler last week.
A small force of tanks went into northern Gaza early on Monday in what the military called a "limited" operation to find explosives and tunnels.
In northern Gaza Israeli air strikes killed one militant, while troops shot dead another, the Associated Press news agency reported.
Israeli aircraft also hit several targets across Gaza, including a building used by the al-Aqsa Martyrs Brigades, a militant group linked to Palestinian President Mahmoud Abbas' Fatah party.