"We must all agree on a joint arms embargo," Foreign Minister José Manuel Albares told journalists at the start of a ministerial meeting of the so-called Madrid Group in the Spanish capital on Sunday.
"The last thing the Middle East needs right now is weapons."
Israel has blocked the import of all food, medicine and fuel for two and a half months before letting a trickle of aid enter last week, after experts' warnings of famine and pressure from some of Israel's top allies.
Albares also called for an immediate suspension of the European Union's partnership agreement with Israel - a measure currently being considered in Brussels.
He also wants to impose targeted sanctions against individuals "who obstruct the two-state solution".
If necessary, sanctions should also be imposed against Israeli Prime Minister Benjamin Netanyahu, Albares said.
"Nothing that is being discussed here is directed against the State of Israel," the top Spanish diplomat emphasised.
But he also made it clear that "the Palestinian people have exactly the same right to peace and security as the Israeli people".
There is no alternative to the two-state solution for achieving lasting and just peace, Albares said.
In an interview with French broadcaster France Info shortly before, the minister had said: "What is the alternative? Kill all Palestinians? Drive them... I don't know where... to the moon? ... Or give them Israeli citizenship?"
The Spanish government is one of the harshest critics in Europe of Israel's military action in Gaza.
Hamas-led militants killed some 1200 people, mostly civilians, in the October 7 attack and abducted 251 people.
Around a third of the remaining hostages are believed to be alive, after most of the rest were released in ceasefire agreements or other deals.
Israel's 19-month offensive has killed over 53,000 Palestinians, according to Gaza's Health Ministry, which says women and children make up most of the dead.
It does not provide figures for the number of civilians or combatants killed.
The offensive has destroyed vast areas of Gaza and displaced around 90 per cent of the territory's population, often multiple times.
with AP