Islamic Jihad, another Gaza-based Palestinian group, said that it had fired one of the rockets that hit Tel Aviv.
Late on Thursday, Israel began moving troops towards the Gaza Strip and Ehud Barak, the Israeli defence minister, authorised the call-up of 30,000 reservists for a possible ground invasion.
At least a dozen lorries carrying tanks and armoured vehicles were seen moving towards the border area, while buses ferried soldiers.
While southern Israeli areas near Gaza have long coped with rocket fire, the attacks on the Tel Aviv area illustrated the significant capabilities that Hamas has developed.
Palestinian fighters had previously hit Rishon Lezion before but never reached Tel Aviv, roughly 70km north of the Gaza Strip.