A couple of years ago, Rabbi Norman Lamm, the respected chancellor of Yeshiva University, caused a stir when he predicted the demise of non-Orthodox Judaism in the USA. It would soon be time to say Kaddish over the Conservative and Reform movements, he told the Jerusalem Post.

Certainly, Conservative Judaism appears to be in the grip of accelerating decline. By the beginning of the century, its share of synagogue-affiliated Jews in the USA had dropped from 43 per cent to 33 per cent in 10 years, losing its place to Reform as the country's largest Jewish stream. But then it would be premature to write off a movement that can still claim around one and a half million members and that can produce rabbis like David Wolpe.

The senior rabbi of the Sinai Temple in Los Angeles was ranked number two this year in Newsweek and the Daily Beast's annual list of America's top 50 rabbis - the highest placed rabbi with a pulpit. His shul attracts a thousand worshippers on a Shabbat morning. He is the author of a seven books and contributor to national media such as the Washington Post and the online Huffington Post. His 10,000 Facebook followers can access his weekly Off the Pulpit email which demonstrates the virtue of a pithy style and an easy turn of phrase.

His profile has also risen through being prepared to wage the case for God in public debates with the archdukes of atheism, Richard Dawkins, Christopher Hitchens and Sam Harris. His 2008 book Why Faith Matters was prompted by the intellectual challenge posed by the new adversaries of religion but also by more personal circumstances.

"It started after I finished treatment for cancer," he said. "I had two agendas on my mind. One was the recent spate of atheism. The other was a response to what I had just undergone and talk about how a faith that wasn't credulous or fundamentalist dealt with such life crises."

As for Lamm's pessimism, he counters with the observation that "the most perilous enterprise is prophecy and extrapolating from current trends is as foolish in religion as it is in economics".

The growth of Orthodoxy may reflect a "worldwide wave of more traditional forms of religion and it would be surprising if Judaism didn't take after that. But I don't think a wave is eternal.

"As the intellectual pressures of Western society increase, I am hoping you will see a gradual defection from fundamentalism and that - unbeknownst to all these yeshivot - they are training the next generations of Conservative Jews. It has happened before and it may happen again."

But he is unhappy with the label "Conservative", a catch-all term for people who wanted to be traditional but non-Orthodox but missing what he believes is the essence of the movement. "I think the time has long past that we need to provide a positive, as opposed to a passive, definition of what we are," he said.

His own suggestion is for renaming it Covenantal Judaism because "I think conservatism is the Judaism of relationship. We believe in relationship with other Jews, with the non-Jewish world, with Israel, with God. We don't sever ties with any other group and I think our interpretation of the mitzvot is that they are intended lekarev, to draw us closer."

Although the Conservative movement is affiliated to the worldwide Masorti Olami, he doubts whether the name Masorti would "catch on in America". The Conservative movement remains more liberal in practice than Masorti in Israel or in the UK. His own synagogue, 106 years old, has always had an organ - although it has an alternative minyan which does not use instruments. Female Conservative rabbis have been ordained for 20 years.

"You could not have an effective non-Orthodox movement in America that was non-egalitarian," he said.

And as for the question of gay marriages, he argues that "in America in 10 years, maybe less, maybe more, it won't be an issue. The sociological trend is overwhelming. Under [the age of ] 30, 70 per cent favour gay marriage; under 18, it is probably 90 per cent. It is almost irrelevant what your view is, you are standing against the ocean in America and I suspect that will be true of Europe, too."

Theologically, there are different Conservative teshuvot on the subject. "You can argue, especially if you use biblical criticism, that what the Bible was proscribing was not necessarily gay relationships."

Openly gay and lesbian students are already admitted to the American Conservative rabbinic institutions, the Jewish Theological Seminary and the American Jewish University. "Gay marriage is a matter of time," he said, "whether one likes it or not."

He visited the UK earlier this summer to deliver the annual memorial lecture for Rabbi Louis Jacobs. But he also dropped in to Tony Blair's Faith Foundation and saw Chief Rabbi Lord Sacks.

He is an admirer of the Chief Rabbi's writings, describing him in a recent review as the "most gifted expositor of Judaism today" and a "masterful interpreter" of Torah, who is best placed to give contemporary Judaism what it currently lacks: a comprehensive philosophy. But he also has his criticisms, saying that Lord Sacks's ignoring of comparative religion, archaeology, history and textual criticism of the Bible has left a "gaping hole" in his work.

And the Chief Rabbinate is not a model to emulate. In the US, "a Conservative synagogue will partner with an Orthodox synagogue for certain things, or a Reform synagogue for certain things. This has to do with the fact there is no Chief Rabbinate so each rabbi can make Shabbes for himself.

"One of the reason why religion thrives in America is precisely because there has never been an official church. So competition is good for religion as it is for everything else."