Mr. Siniora spoke hours after gunmen shot and killed the industry minister in a Christian neighborhood near Beirut Tuesday.
The international community has condemned the assassination. The United States calls the killing an act of terrorism and intimidation against Lebanon's elected government.
Gemayel is one of several anti-Syrian politicians to be murdered in Lebanon in the past two years.
Syria has denied any role in his assassination, as well as the other killings. Late Tuesday, diplomats say the UN Security Council approved plans for a special international tribunal to try suspects in last year's assassination of former Lebanese Prime Minister Rafik Hariri. Lebanon's government must approve the tribunal.
A UN. inquiry has implicated Syrian officials in the Hariri killing.
Six pro-Syrian cabinet members recently resigned to back the Shi'ite militant group Hezbollah's demand for veto power. Hezbollah has called for an end to Mr. Siniora's government.
UN Secretary-General Kofi Annan praised Pierre Gemayel as someone who believed strongly in an independent, democratic and united Lebanon.
President Bush said the United States supports the Lebanese government's efforts to defend itself against what he called attempts by Syria, Iran and allies to foment instability and violence in Lebanon. He called for a full investigation into Tuesday's attack.
The European Union called on all parties to avoid actions that would destabilize Lebanon.
Information for this report is provided by AP, AFP and Reuters
