The draft found support among all the 15 council members except Washington.
"The members realised this morning that they cannot reach a consensus concerning this," Giadalla Ettalhi, Libya's envoy and the council chair for this month, said.
"Why the United States rejected the amendments produced by Libya, I think this is a question to be put to them."
Alejandro Wolff, the US deputy ambassador, said that the statement failed to address the core issue, the "illegal coup usurping power from the legitimate Palestinian Authority by the terrorist group Hamas".
Hamas seized full control of the territory after forcing out security forces loyal to Mahmoud Abbas, the Palestinian president, in June last year.
The Israeli blockade had triggered worldwide condemnation, with many countries saying it amounts to the "collective punishment" of Gaza's 1.5 million residents in retaliation for rocket attacks from Palestinian armed groups.
"It is very unfortunate that the Security Council was unable to [agree] a simple statement," Ryad Mansour, the Palestinian observer at the UN, told reporters.
The US delegation on Friday proposed a series of amendments that resulted in a near consensus, that proposal was acceptable to every council member except Libya.
Libya, the only Arab state on the Security Council, offered a counterproposal on Monday but Washington and other countries said it was unacceptable because it failed to condemn the attacks against Israel sharply enough.
"It is imperative not to equate acts of self-defence with terrorist rocket attacks," Wolff said when asked about his objections to the Libyan counterproposal.
The deadlock at the UN came as Abbas and Hamas officials prepared to hold separate talks in Cairo on restoring order at the border between Egypt and Gaza.
Hundreds of thousands of Palestinians have poured across the border to buy food and other basic necessities since Hamas fighters blew holes in the fence last week.
Hamas has said that it must have a role in the control of the Rafah crossing between Egypt and Gaza.
But Abbas has proposed taking over all of Gaza's crossings with Egypt and Israel despite not having a security presence in the Gaza Strip.