On the eve of polling, Mr Price was given a considerable boost when the Guatemalan Foreign Minister, Arturo Fajardo, announced that his country, which has a claim to Belizean territory written into its constitution, would continue to recognise Belize as an independent country.
Mr Price called the election to seek a new mandate after Britain confirmed last month that it was running down its military presence in its former colony, and the president of Guatemala, Jorge Serrano, seized dictatorial powers with military backing a few days later.
This set alarm bells ringing in Belize, as the Guatemalan military have traditionally been the fiercest proponents of Guatemala's century-old claims on the territory of the former British Honduras, on the Caribbean coast of Central America.
But Mr Serrano's dictatorship only lasted a few days, and his replacement on 1 June by Ramiro de Leon Carpio, a leading human-rights campaigner, helped to defuse tension in Belize. Mr Fajardo also announced this week that he would be setting up a 'Council for Belize' to define Guatemala's position in negotiations to resolve remaining border-demarcation disputes. Belize became independent in 1981, but as part of the independence settlement Britain kept a military presence to discourage the Guatemalans from military adventures.
But since Guatemala formally recognised the independence of Belize in 1991, Britain has come to feel the deterrent is no longer necessary.
Last month London announced that the 1,500-strong Belize garrison would be reduced over the next year or so, leaving only a 200-strong jungle warfare training unit. Responsibility for defence will then be in the hands of the 600-man Belize Defence Force.
Despite this week's assurances, the possibility of further sudden changes in Belize's much bigger and much more powerful neighbour, with a population of 10 million to Belize's 230,000, still cannot be ruled out.
Guerrilla warfare has been going on in Guatemala for more than 30 years, during which time some 100,000 people have died, and the 37,000-strong Guatemalan army has a notoriously bad human-rights record. But there are signs that things should improve.
President de Leon took action this week to consolidate his authority over the armed forces by replacing the hardline Defence Minister, General Roberto Perussina, with the more moderate General Mario Enriquez, who opposed the coup by Mr Serrano and who has taken part in peace negotiations with left-wing guerrillas.
Mr Price, 74, of mixed Welsh and Mayan descent, has dominated Belizean politics since long before independence, and his ruling People's United Party is expected to win comfortably today against Manuel Esquivel's divided and demoralised United Democratic Party.