The dispute flared last month when Mexican President Felipe Calderon accused Mr Pascual of "ignorance".
He said the US cables, released by Wikileaks in December, had harmed ties.
The US is backing Mexico's war against drug-trafficking with more than $1bn (£600m) in equipment and training.
The two countries have also increasingly been sharing intelligence in a bid to tackle the drug gangs as violence continues to take a heavy toll in Mexico, with more than 34,000 killed since late 2006.
It emerged earlier this month that the US has been sending unarmed surveillance drones over Mexico to gather information on the major drug traffickers.
US Secretary of State Hillary Clinton said Mr Pascual had decided to step down due to "his personal desire to ensure the strong relationship between our two countries and to avert issues raised by President Calderon that could distract from the important business of advancing our bilateral interests".
She said she and President Barack Obama had accepted his resignation with "great reluctance".
Mr Pascual's decision to leave comes less than a fortnight since Mr Calderon held talks with President Barack Obama in Washington.
The Mexican president had not hidden his anger at the remarks made by Mr Pascual in the diplomatic cables, and reportedly asked for the ambassador to be removed from his post.
"I do not have to tell the US ambassador how many times I meet with my Security Cabinet. It is none of his business. I will not accept or tolerate any type of intervention," Mr Calderon said in February, in an interview with Mexico's El Universal newspaper.
"But that man's ignorance translates into a distortion of what is happening in Mexico , and affects things and creates ill-feeling within our own team."
Mr Calderon also told the Washington Post that bilateral relations had suffered "serious damage" because of the US diplomatic cables.
The Mexican presidency said on Saturday that ties between the two countries remained solid despite Mr Pascual's resignation.
In his cables, released by Wikileaks and published by The Guardian newspaper, Mr Pascual questioned whether President Calderon could win his war on drugs, saying the various security agencies were often at odds.
The Mexican security forces, he said, were slow and risk-averse.
Mr Pascual, a Cuban-American expert in failed states, is a career diplomat.
He recently began dating the daughter of a senior member of Mexico's main opposition party, the Institutional Revolutionary party or PRI.