"I think that ministers have to be confident in their own personal beliefs and it would be wrong for them to do something they disagree with," Mr Armstrong said.
God intended marriage to be between a husband and wife, he said.
"I feel that by opening it up to include people who aren't included in God's definition, it is diluting the institution as it has been upheld in the past," he said.
Mr Armstrong said he would not marry a same-sex couple due to his personal views and thought most Baptist pastors would feel the same way.
Reverend Paul Williamson, co-vicar of Holy Trinity Church, said he would also make use of the amendment if passed into law.
"I am not in favour of same-sex marriage. Marriage by definition, by historic nature, and by theological understanding is a male and female covenant, and civil unions provide all necessary social and legal definition and protection for those in a same sex relationship," he said.