Planners have already approved the development at Ballynakelly, near Coalisland.
Mid-Ulster Council's planning committee met on Tuesday evening.
It said it would delay its decision until members visited a similar plant.
Councillors also want to view the site at Ballynakelly.
Several hundred people have written to the Planning Service to oppose it.
The proposal would see a 500KW digester that would take 10,950 tonnes of silage and 1,450 tonnes of slurry a year. It would treat it in sealed units to create gas which would be used to produce power. The residue would be returned to farms for spreading.
Documents submitted as part of the planning process show that there would be around 10 loads a week of material arriving at the facility, which is 100 metres from a housing development of 31 homes and a children's playground.
Callan Renewables Ltd, which is behind the scheme, said the facility would generate enough renewable electricity to power 500 homes.
Locals opposed to the development have sent letters to the planners saying it is "large-scale, commercial and out of character with the surrounding local area".
Callan Renewables Ltd defended the location of the site.
"Despite suggestions that the plant is located within an established residential area, the site is located within an industrial area with the nearest residential property circa 150 metres away," the company said in a statement.
Planners said that as the plan would entail the extension of a farmyard already used for industrial purposes, the proposal would not have a "negative impact on the character of the area".
They also said that as the plant would use methane gas from slurry, which would otherwise be released into the environment, it would be of benefit and in line with current government policy on meeting renewable energy targets.
But DUP peer Lord Morrow said he was "amazed" that planners had approved the proposal.
"It appears that the planners are choosing to ignore the will of the local community, who have voiced their objections totalling well over 500 submissions," he added.
"I cannot recall another application in the South Tyrone area attracting so many objections."
Councillors have deferred a decision on whether to give the go-ahead for a commercial waste digestion and power plant that objectors claim would be too close to homes in a small County Tyrone village.