Tom Casey, a US State Department spokesman, said parties to the nuclear deal were still committed to getting a "full and complete" declaration from Pyongyang.
"The declaration is critical," he said.
"This can't be a situation where they pretend to give us a full declaration and we pretend to believe them. This has to be full and complete and that's why, I think, this is taking extra time."
"This can't be a situation where they pretend to give us a full declaration and we pretend to believe them"
US state dept spokesman
In North Korea's message, carried as an editorial across state media on Tuesday, it called for an end to "the US policy hostile towards the DPRK", or the Democratic People's Republic of Korea, the formal name for North Korea.
But it added the North was ready to develop "relations of friendship and cooperation with all the countries that are friendly toward it".
It also called for the armistice signed at the close of the 1950-53 Korean War to be replaced by a peace treaty.
The absence of a formal treaty means the Korean peninsula is still technically at war.
It its message the North said it would "make earnest efforts for stability on the Korean peninsula and peace in the world" and called for the abolition of US military bases in the South.
"Inter-Korean cooperation is a noble patriotic undertaking," the message said.
"The idea of confrontation regarding the fellow countrymen as the archenemy should be discarded"
North Korean editorial
"The idea of confrontation regarding the fellow countrymen as the archenemy should be discarded, the military tension be eased, and the elements of dispute be removed."
Following the missed deadline, the US and South Korea said they expected the overall disarmament process to be behind schedule but still on track.
According to analysts, by letting the deadline pass North Korea could be trying to extract further concessions from the US.
US intelligence experts estimate North Korea has produced enough plutonium for about eight nuclear weapons.
They also believe it has operated a separate secret programme to enrich uranium for weapons.
Nuclear weapons can be built either with plutonium produced in a reactor, or by enriching uranium – a process which does not require a reactor.
However, few US officials seem to believe the North is prepared to see the denuclearisation agreement collapse entirely.
"The important thing is not whether we have the declaration by today," Tom Casey, the US state department spokesman, told reporters on Monday
"The important thing is that we get a declaration that meets the requirement of the agreement, which means it needs to be full and complete."