He said that, based on intelligence, the Israeli army believed the tunnel belonged to Hamas, the militant organization that runs Gaza. The alleged incident took place near Beit Lahiya.
Gazan residents said the strike was in the north of the Palestinian enclave.
Palestinians say the two killed were members of the Al-Quds Brigade, the military wing of Islamic Jihad.
The terrorist group said in an official statement that it "mourned" the loss of its two members. The Israeli military had no immediate comment.
Israeli planes and tanks shelled the Palestinian territory on Monday after the rocket strike, in what was the latest in a series of cross-border exchanges that have left at least four Palestinians dead.
"The IDF holds Hamas responsible for these aggressive acts", the spokesman wrote.
However, the Israeli army on Tuesday denied it carried out the air strike, according to reports. -Gen. Ronen Manelis said, adding that "the tunnel project in the Gaza Strip has suffered a heavy blow".
The IDF said the Iron Dome successfully intercepted the rocket.
"In response to the rocket, an IDF tank and the IAF [Israel Air Force] targeted Hamas terror posts in the southern Gaza Strip", the tweet said.
The announcement, cleared by Israeli censors who had previously barred reports of detection work around the central Gaza frontier, followed a surge of Palestinian unrest in response to last week's U.S. recognition of Jerusalem as Israel's capital.
There was also no word on injuries on the Gaza side of the border. A third rocket was intercepted by an Iron Dome system.