The death toll reached 24 on Thursday, with another 13 still seriously hurt.
Dozens of family members gathered near the gates of the plant to demand talks with plant bosses.
Some tried to force their way into the compound, the Associated Press news agency reported.
Mexico`s state oil company Pemex raised the death toll late on Wednesday, and said 19 people remained in hospital.
Rosa Villalobos travelled four hours to search for her son who worked at the plant, but could not find him at the hospital.
"What I want is for justice to be done in my son`s case, for there to be no impunity," she told AP.
"I`m going to stay here. Even though I have no money, even though I have nothing to eat, I`m staying put."
Ancelma Cordero`s 21-year-old brother is one of the missing. "We are desperate because no-one is coming out to show their face," she told Reuters at the plant gates.
"They told us we were breathing toxins and we should leave. But ... if we leave, they could make the bodies disappear."
President Enrique Pena Nieto, who spoke of "a tragic accident", travelled to the site late on Thursday.
The director of Pemex, Jose Gonzalez Anaya, said the explosion "was caused by a leak" but "we don`t know how that leak occurred".
The incident occurred at around 15:15 local time (20:15 GMT) on Wednesday. Veracruz state Governor Javier Duarte told a radio station the blast was felt 10km (six miles) away.
More than 130 people were injured and thousands had to leave their homes.
The head of Mexico`s emergency services, Luis Felipe Puente, had earlier said 10 bodies were found when his staff entered the site.
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Residents were told to stay indoors because of the possible toxic nature of the smoke from the blast, but Pemex said the smoke dissipated quickly, lessening any possible toxic effects.
On Thursday the company said there was no longer any danger from the smoke.
AP reported that the plant produces vinyl chloride, a dangerous chemical used to make PVC pipes and packaging materials.
In September 2012, an explosion then a fire at a gas plant in the northern state of Tamaulipas killed 33 people.
Pemex`s own headquarters in Mexico City was hit by a large gas blast in January 2013, killing 37 people.
A number of fires also struck the company`s rigs in the Gulf of Mexico last year, and a worker was killed in another fire at the Veracruz plant in February this year.