Predicting extreme weather events such as tropical and extratropical cyclones is of vital scientific and societal importance. Of late, machine learning methods have found their way to weather analysis and prediction, but mostly, these methods use machine learning merely as a complement to traditional numerical weather prediction models. Although some pure machine learning and data-driven approaches for weather prediction have been developed, they mainly formulate the problem similar to pattern recognition or follow the train of thought of traditional time-series models for extreme weather event forecasting; for the former, this usually yields only single-step ahead prediction, and for the latter, this lacks the flexibility to account for observed weather features as such methods concern only the patterns of the extreme weather occurrences. In this paper, we depart from the typical practice of pattern recognition and time-series approaches and focus on employing machine learning to estimate the probabilities of extreme weather occurrences in a multi-step-ahead (MSA) fashion given information on both weather features and the realized occurrences of extreme weather. Specifically, we propose a Markov conditional forward (MCF) model that adopts the Markov property between the occurrences of extreme weather for MSA extreme weather forecasting. Moreover, for better long-term prediction, we propose three novel cube perturbation methods to address error accumulation in our model. Experimental results on a real-world extreme weather dataset show the superiority of the proposed MCF model in terms of prediction accuracy for both short-term and long-term forecasting; moreover, the three cube perturbation methods successfully increase the fault tolerance and generalization ability of the MCF model, yielding significant improvements for long-term prediction.