Same-sex marriage plans to be outlined
The government is to publish on Tuesday details of how it intends to introduce same-sex marriage.
Last week David Cameron said he wanted churches in England and Wales - which had originally been excluded - to be part of the plans.
Ministers said any changes would "fully respect" the rights of religious organisations who did not want to carry out same-sex ceremonies.
The plans have divided Tory MPs, but are backed by Labour and the Lib Dems.
The Church of England and Roman Catholics, among other denominations, have voiced opposition to same-sex marriage.
But some religious groups, including Quakers, Unitarians and Liberal Judaism, are in favour of gay marriage and are thought likely to apply to be allowed to stage ceremonies.
The government's initial consultation document said it would not be possible for a same-sex couple to get married in church and other religious premises.
But under new proposals, to be outlined by Mrs Miller, this is expected to be permitted.
Religious organisations which do not want to host same-sex weddings will be given an absolute guarantee that they will not be forced to do so.
Mrs Miller told MPs she fully supported the institution of marriage and said extending marriage to same-sex couples would "make sure marriage is relevant for our century".
"The government should not stop people getting married unless there is a very good reason. Being gay, I don't believe, is one of them," she said.
She insisted that religious freedom would be protected, adding that "the views of people of faith should not be marginalised and should be fully respected".
The plans had been drafted so there was a "negligible" chance of religions which did not want to carry out gay marriages facing a legal challenge, she said.
For Labour, Yvette Cooper backed the change, saying: "Marriage is not the preserve of any individual faith or organisation.
"Civil marriage is about the way the state views and values long-term relationships and the state should not discriminate."
Allowing same-sex marriages would "strengthen rather than weaken the institution of marriage", she added.
Ms Cooper called for those faiths who wanted to be able to celebrate same-sex marriage to be able to do so.
Plans to legalise same-sex marriage have divided the Conservative Party and more than 100 Tory MPs are thought to be against the idea.
Edward Leigh, MP for Gainsborough, said the state had "no right to redefine people's marriages" and allowing same-sex marriages in churches would "gravely increase" the chance of human rights litigation forcing churches to comply.
Bob Stewart, Conservative MP for Beckenham, said the government was risking upsetting thousands of people in "normal marriages".
But a number of senior Tories including Education Secretary Michael Gove, London Mayor Boris Johnson and former Prime Minister John Major have backed same-sex marriage by religious bodies.