US officials have warned that the Bush administration can take action against financial institutions that help provide money or services directly to the new government.
As the United States has designated Hamas as a "terrorist" organisation, such actions could be in breach of US law.
Washington has been spearheading a campaign with Israel to isolate Hamas, which won elections in January and took control of the Palestinian Authority late last month.
US officials would not discuss any specific communications with banks regarding the Islamic militant group, whose charter calls for Israel's destruction.
But without commenting specifically on any US or foreign banks, Molly Millerwise, the US Treasury Department spokeswoman said: "If an organisation or individual is facilitating direct fundraising for Hamas, they open themselves up to action by the United States."
Nabil Amr, a top adviser to Palestinian president, said: "there are warnings to the banks not to deal with the money coming to the Palestinian people and the Palestinian Authority."
Banks in the region rely heavily on "correspondent" financial institutions in the United States to conduct day-to-day transactions.
"If an organisation or individual is facilitating direct fundraising for Hamas, they open themselves up to action by the United States"
Nabil Amr, adviser to President Mahmoud Abbas
Palestinian officials said these regional banks were concerned that Washington would put pressure on Wall Street banks to sever these correspondent ties if they helped transfer funds to the Palestinian Authority.
These US banks include JP Morgan, Citibank, Bank of New York and American Express, among others.
Shunned by the West and increasingly strapped for cash, Hamas has made urgent appeals in recent days to Iran and Arab donors to deposit funds in bank accounts in Egypt. The government is already three weeks late in paying salaries to 165,000 government workers.
Recently Qatar and Iran were the latest Muslim countries to donate money to the new government with Doha donating $50 million and Tehran promising to give at least $50 million.
Hamas officials say the United States triggered the financial crisis by pressing the Amman-based Arab Bank to freeze the Palestinian Authority's main treasury account.