Yes. Both countries have a full diplomatic relationship established; both have embassies and both have a small but ongoing trade office at each other's capital city.
That would be most countries where Mexico does not have a direct representation (i.e. where Mexico has no embassy nor diplomatic relations). That would include most African countries such as Mozambique or Libya and some Central and South Asian countries, such as Kazakhstan, Mongolia and Papua New Guinea.
Mexico refused to recognize the annexation.
c. Texas
Mexico broke off diplomatic relations with the United States after the annexation of Texas in 1845. The annexation was a significant factor leading to heightened tensions between the two nations, ultimately culminating in the Mexican-American War (1846-1848). Mexico viewed the annexation as an act of aggression and a violation of its sovereignty.
In 1961 the US ended diplomatic relations with Cuba.
Breaking diplomatic relations means that two countries have broken ties between each other. In 1964, the United states broke diplomatic relations with Cuba due to changes in leadership.
NO
Cuba, Libya, Iran, and North Korea are the only countries not to have diplomatic relations with the US.
Restoring diplomatic relations involves the mutual agreement of two countries to resume formal diplomatic ties, including the reopening of embassies and the exchange of ambassadors. This process usually involves negotiations to address any outstanding issues that led to the breakdown of relations. Once an agreement is reached, a formal announcement is made, and the diplomatic relations are restored.
relations
1794
The primary Mission of the State Department is Diplomacy