UK Chancellor Gordon Brown has ordered British banks to freeze the assets of Hamas' new leaders, including Abdel Aziz al-Rantissi.
Mr Rantissi is regarded as a hardliner and a firebrand orator
Khalid Meshaal, the man named as the overall leader of the Palestinian militant group, was also targeted.
Mr Rantissi, took over as head of Hamas in Gaza after the death of Sheikh Ahmed Yassin in an Israeli missile attack.
Palestinian leader Yasser Arafat, meanwhile, urged an end to the killing of Israeli and Palestinian civilians.
After a meeting with European Socialist politicians on Wednesday, Mr Arafat made a renewed call for international monitors to be allowed in to supervise and help defuse the tense situation between Israel and the Palestinians.
There have been fears that a new wave of violence may erupt amid threats from armed Palestinian groups to retaliate for the death of Hamas founder Yassin on Monday.
And following a wave of international condemnation of the killing, the UN Commission on Human Rights passed a resolution strongly condemning "liquidations" and "extra-judicial killings", including the assassination of Yassin.
Mr Brown directed the Bank of England to issue instructions to financial institutions to freeze funds belonging to Mr Rantissi and Mr Meshaal, along with Musa Abu Marzouk, Imad Khalil al-Alami and Usama Hamdan.
A statement by the UK Treasury said there were "reasonable grounds" to suspect that they "facilitate or participate in the commission of acts of terrorism", and that Mr Rantissi may also have committed such acts.
UK MEASURES AGAINST TERROR FUNDING
Around £70m ($130m) in terrorist assets frozen
38 bank accounts currently frozen in UK institutions
£3.65m funding for counter-terrorist training abroad
Mr Brown has also asked to freeze assets under the names Kadek and Kongra-Gel, as aliases of the Kurdistan Workers' Party (PKK), outlawed in Turkey and already itself subject to a freeze.
He presented the measures as part of a crackdown on terrorism and urged Europe to do more to act together against those who fund terrorists.
Israel has vowed to kill more top militants, while Mr Rantissi has urged Hamas to avenge Yassin's death.
Israelis "will know no security", Mr Rantissi told crowds of mourners at Gaza's soccer stadium.
He said he was not afraid of Israeli attempts to kill him.
"If it's cardiac arrest or an Apache (helicopter), I prefer to be killed by an Apache," Mr Rantissi told reporters.
Mr Rantissi later made it clear that Hamas had no plans to attack US targets, apparently backing away from veiled threats issued after Yassin's death.
He told reporters in Gaza that Hamas activities were aimed solely at Israel.