Recently, reasoning-based MLLMs have achieved a degree of success in generating long-form textual reasoning chains. However, they still struggle with complex tasks that necessitate dynamic and iterative focusing on and revisiting of visual regions to achieve precise grounding of textual reasoning in visual evidence. We introduce \textbf{VLM-R3} (\textbf{V}isual \textbf{L}anguage \textbf{M}odel with \textbf{R}egion \textbf{R}ecognition and \textbf{R}easoning), a framework that equips an MLLM with the ability to (i) decide \emph{when} additional visual evidence is needed, (ii) determine \emph{where} to ground within the image, and (iii) seamlessly weave the relevant sub-image content back into an interleaved chain-of-thought. The core of our method is \textbf{Region-Conditioned Reinforcement Policy Optimization (R-GRPO)}, a training paradigm that rewards the model for selecting informative regions, formulating appropriate transformations (e.g.\ crop, zoom), and integrating the resulting visual context into subsequent reasoning steps. To bootstrap this policy, we compile a modest but carefully curated Visuo-Lingual Interleaved Rationale (VLIR) corpus that provides step-level supervision on region selection and textual justification. Extensive experiments on MathVista, ScienceQA, and other benchmarks show that VLM-R3 sets a new state of the art in zero-shot and few-shot settings, with the largest gains appearing on questions demanding subtle spatial reasoning or fine-grained visual cue extraction.