United States negotiators reported further progress yesterday toward a deal with Iran to bring about release of the 52 American hostages, with money still the immediate obstacle to agreement.

As another day ticked by toward Friday, which the Carter administration has described as the last chance for acceptance of an arrangement which could be implemented before it leaves office, Deputy Secretary of State Warren Christopher issued a public note of caution against optimism "because fundamental differences remain to be resolved."

Christopher, who was meeting in Algiers with the authorized Algerian intermediairies, also sent back word to Washington, as reported by State Department spokesman John Trattner, that "progress continues to be made on several aspects of the highly complex issues."

Informed sources said the Carter administration has provided Iran with additional details of its final offer, which calls for $7.3 billion in Iranian assets to be released to Tehran at the time the hostages are freed, and another $2.2 billion in Iranian assets to be provided later under a claims settlement arrangement.

It is unclear whether Iran will agree to this timetable for return of its money, which was frozen by white house order following the seizure of the Americans more than 14 months ago. the U.S. argument is that Iran would be better off to take what it can, as quickly as it can, under this formula than to hold on to the hostages in vague and probably forlorn hopes of a more acceptable accommodation in the Reagan administration.

The United States is reported to be working, through the Algerian intermediairies, on details of a three-way American-Algerian-Iranian executive agreement to be implemented this week governing the release of the hostages and the return of the Iranian funds. Iran's reluctance to sign a document with the "Great Satan," as the United States is called in Tehran, may be overcome by such ingenious legalisms as the signing of three separate pieces of paper in the three capitals.

As seen in official circles here, the fate of the Carter administration's plan and the immediate future of the captive Americans rest on the ability of the Tehran authorities to establish and enforce a consensus long enough to take the hard decision to accept the American terms and release the hostages.

In this perspective, the decision by Iranian leaders to seek additional negotiating authority from the Majlis, or parliament, was seen here as a sign of seriousness of purpose. But the postponement of the Majlis deliberations yesterday, because some essential officials were absent, touched off new concern in Washington.

It was not known whether the absences reflected an attempt by some Iranian factions to torpedo an agreement. With the Friday deadline just ahead, however, some here who were already wary downgraded their estimates of the likelihood of immediate success. State Department officials also noted that Ayatollah Ruhollah Khomeini has yet to endorse acceptance of the American proposals, and his endorsement probably will be necessary for final approval by the Iranian body politic. Khomeini has been an insurmountable obstacle to release of the hostages on U.S. teams in earlier sequences. Should Iran gather its political will and accept American terms by the signing of an executive agreement, the United States would act to move $7.3 billion in blocked Iranian funds to the hands of a third country, which may not be Algeria. This action is likely to take several days of legal maneuvering. The transfer of about $1.8 billion of this sum, from American banks abroad, would require arrangements by Iran to pay smaller debt-service charges to the banking institutions.

Once the sums are in the hands of the authoried "escrow" holder, the next step would be release of the 52 Americans, and the simultaneous release to Iran of the money being held for it.

The Carter administration is making its maximum effort to bring about the simultaneous release of the hostages and the money before relinquishing the reins of government Tuesday. In practical terms, this would require completion of the detailed agreement by Friday.

If Iran is unwilling or unable to agree in the time allowed, the Reagan administration will assume power Tuesday with all its options intact, including suspending or breaking off the negotiations and withdrawing the Carter administration's proposals.

If a deal is on the verge of completion, except for a last-minute snag, the Reagan administration will have the option of permitting the Carter negotiating team to finish the job, or of taking over that final task with the aid of consultants from the Carter team. This remains a remote but theoretical possiblity as Iran heads into its most crucial three days of decision-making about the captive Americans.